Timeline for Are the tangle functors based off Khovanov homology braided monoidal functors?
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6 events
| when toggle format | what | by | license | comment | |
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| May 3, 2020 at 14:25 | comment | added | Andy Nguyen | @Adrien Thanks a bunch! | |
| May 3, 2020 at 10:22 | comment | added | Adrien | Yes, any reasonable definition of braided monoidal 2-category should coincide with the notion of $E_2$-algebra in the (3,1)-category of 2-categories. For Khovanov homology I suppose you want something like a symmetric monoidal $(\infty,1)$-category of presentable dg-2-categories which I have no clue how to define (but I'm sure some people have thought about it). Then indeed you can use the framework of factorization homology to attach 2-categories to (oriented if you have a framed $E_2$-algebra) surfaces. What's more tricky, AFAIK, is how to define the correct version of ribbon 2-category. | |
| May 1, 2020 at 11:08 | comment | added | Andy Nguyen | @Adrien Thanks for the Help! I have actually be trying to learn your work "Integrating Quantum Groups over Surfaces" with Ben-Zvi and Jordan. I was wondering if given a braided monoidal 2-category, would one be able to get an $E_n$-algebra? And use the factorization homology framework? If the answer is in the positive, which $n$? What would be the analogue of $Pr_c$? | |
| Apr 29, 2020 at 11:03 | comment | added | Adrien | It definitely doesn't comes from a braided monoidal functor. We hope it comes from a braided monoidal 2-functor, but before asking this question you'd need a braided monoidal 2-category structure on the target, and AFAIK (I'm not an expert on this) we're not there yet, although there has been a lot of work in that direction. | |
| Apr 29, 2020 at 10:55 | review | First posts | |||
| Apr 29, 2020 at 11:16 | |||||
| Apr 29, 2020 at 10:52 | history | asked | Andy Nguyen | CC BY-SA 4.0 |